Structure-transport analysis for particulate packings in trapezoidal microchip separation channels

Abstract

This article investigates the efficiency of particulate beds confined in quadrilateral microchannels by analyzing the three-dimensional fluid flow velocity field and accompanying hydrodynamic dispersion with quantitative numerical simulation methods. Random-close packings of uniform, solid (impermeable), spherical particles of diameter d_p were generated by a modified Jodrey–Tory algorithm in eighteen different conduits with quadratic, rectangular, or trapezoidal cross-section at an average bed porosity (interparticle void fraction) of ε = 0.48. Velocity fields were calculated by the lattice Boltzmann method, and axial hydrodynamic dispersion of an inert tracer was simulated at Péclet numbers Pe = u_avd_p/D_m (where u_av is the average fluid flow velocity through a packing and D_m the bulk molecular diffusion coefficient) from Pe = 5 to Pe = 30 by a Lagrangian particle-tracking method. All conduits had a cross-sectional area of 100d_p² and a length of 1200d_p, translating to around 10⁵ particles per packing. We present lateral porosity distribution functions and analyze fluid flow profiles and velocity distribution functions with respect to the base angle and the aspect ratio of the lateral dimensions of the different conduits. We demonstrate significant differences between the top and bottom parts of trapezoidal packings in their lateral porosity and velocity distribution functions, and show that these differences increase with decreasing base angle and increasing base-aspect ratio of a trapezoidal conduit, i.e., with increasing deviation from regular rectangular geometry. Efficiencies are investigated in terms of the axial hydrodynamic dispersion coefficients as a function of the base angle and base-aspect ratio of the conduits. The presented data support the conclusion that the efficiency of particulate beds in trapezoidal microchannels strongly depends on the lateral dimensions of the conduit and that cross-sectional designs based on large side-aspect-ratio rectangles with limited deviations from orthogonality are favorable.